# Transition Information Density: Morphological Trajectories, Synesthetic Perception, and Structured Interpolation in Neural Training (or: The Synesthetic AI)

arXiv: https://arxiv.org/abs/2607.03210 · HTML: https://mlsanity.com/paper/2607.03210/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 5 references that are in the map.
- First posted on arXiv 3 Jul 2026.

## Builds on (most cited first, 3 of 3)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Local Intrinsic Dimension of Representations Predicts Alignment and Generalization in AI Models and Human Brain](https://mlsanity.com/paper/2601.22722/) (2026)

## Abstract (arXiv)

Standard machine learning training presents data as discrete endpoint pairs, omitting the structure of the space between them. This paper introduces Transition Information Density (TID) -- the information content recoverable from structured intermediate states between categorically distinct training endpoints -- and Positional Identity, the defined location of an intermediate state on the A-to-B continuum. Both constructs are grounded in three empirical contexts: grapheme-color synesthesia, the Synesthesia Grid (a boundary-contour morphing algorithm instantiating TID in visual morphological space), and a four-condition training experiment across four representational mediums. Probes trained on structured interpolation at defined Positional Identities (C3) exhibit substantially lower intrinsic dimensionality than volume-matched controls (C2) in Phonetic/Linguistic (C3: 3.33 vs. C2: 10.81) and Semantic Description (C3: 4.59 vs. C2: 8.67) mediums. Visual and cross-modal mediums do not show this effect, establishing a modality boundary condition. A fixed-N=50 comparison confirms that Positional Identity structure, not sample count, drives the effect. Resolution N scales monotonically with representational richness. Pooled TwoNN analysis reveals globally collapsed representations in visual space (0.075) and globally consistent representations in phonetic space (0.977). The paper contributes a formal definition of TID and Positional Identity, a nine-metric shape characterization framework, and a four-condition experimental design isolating trajectory structure, data volume, and Positional Identity as distinct factors.